Written by current PhD students in mathematics, this calculus study guide contains detailed step-by-step solutions to problems from past tests and exams at the University of Toronto. Based on the MAT 137 course, this handbook was written with the student in mind. While the problems originate from U of T, the material is easily comparable to any introductory university calculus course that has a focus on proofs. For a lighter approach, see the MAT 135/136 guide. After being teaching assistants for calculus courses over several years, Joshua and Sergio found students constantly asking about solutions from other help manuals. The solutions were either wrong or poorly explained. They saw the need for a more comprehensive solution manual that explained every step in detail. Before beginning their PhDs at Columbia and Cornell University respectively, they wrote this study guide to better help students having difficulty with mathematics.